Answer to Question #266192 in Microeconomics for anu

Question

Suppose the supply and demand curves for apples are given by: Qs = -25 + 2P; Qd = 500 - 3P

(a) Calculate the equilibrium price and quantity in

(b) Calculate the consumer surplus given the equilibrium price. Clearly identify the area of consumer surplus on the graph.

(c) Calculate the elasticity of demand and of supply at the equilibrium point.

(d) Given the elasticities you calculated above, could you tell whether a leftward shift of the supply curve would lead to more or less spending on apples? 

(e) Suppose the government introduces a price floor of $130. What is the new equilibrium quantity traded? What is the consumer surplus? Calculate and indicate on the same graph. Are consumers better or worse off by this policy?

(f) If the government decides to buy all excess surplus (resulting from introduction of price floor) of apples in the market how much money it has to spend to clear the market? Explain.

Answer 1

a)At equilibrium, Q_d=Q_s

500-3P=-25+2P

Equilibrium price; P=105

$\therefore$ Q_d=Q_s

500-3(105)=-25+2(105)

Equilibrium quantity, Q=185

b)Graph

Consumer surplus=$0.5\times Q_{d}\times \delta P$

=$0.5\times185\times \ (165-105)$

= 5,550

c) Elasticity of demand and of supply at the equilibrium point.

Elasticity of demand, E_d=$\frac{\delta Q_{d}}{\ deltaP}\times\frac{P}{Q}$

E_d=$-3\times\frac{105}{185}=-1.7$

Elasticity of supply, E_s;

E_s=$\frac{\delta Q_{s}}{\ deltaP}\times\frac{P}{Q}$

E_s=$2\times\frac{105}{185}=1.14$

d)Given the elasticities above, a leftward shift of the supply curve would lead to less spending on apples .As supply decreases, a condition of excess demand is created at the old equilibrium level. Effectively there is increased competition among the buyers, which obviously leads to a rise in the price hence the consumer will purchase less apples due to the price increase.

e)

Using the graph above:

i)The new equilibrium quantity traded will be 230.

ii)The consumer surplus will be:

$=0.5\times(230-110)\times(130-105)$

$=1,500$

iii)Consumers are always worse off as a result of a binding price floor because they must pay more for a lower quantity.

f) How much money it has to spend to clear the market?

The excess surplus is 1500, so the government will have to spend ($1500\times\$130)=\$195,000$